I live in a townhouse condo in Michigan. I noted the the water valve on the toilet was leaking. In attempting to repair it, I shut off the basement water main to the unit. I checked various faucets around the home and confirmed that they were not functioning. I then flushe the toilet and was amazed to see the tank refilled at once. I kept flushimg and the water still came and refilled.

How can I cut off the water flowing to the toilet tank?

If it is just a packing nut you can do that with the water on. If something else is leaking, shut down the house and turn on the faucets and leave them open. As you open the second and success faucet, it will break the vacuum in the system and let it drain. your toilet may have been refilling from gravity, or it may be plumbed into someone else's water system.

My first thought was that the toilets water supply was connected to a different unit.